Parity Systems and the Delta-Matroid Intersection Problem

André Bouchet, Bill Jackson
<span title="1999-09-03">1999</span> <i title="The Electronic Journal of Combinatorics"> <a target="_blank" rel="noopener" href="" style="color: black;">Electronic Journal of Combinatorics</a> </i> &nbsp;
We consider the problem of determining when two delta-matroids on the same ground-set have a common base. Our approach is to adapt the theory of matchings in 2-polymatroids developed by Lovász $[13]$ to a new abstract system, which we call a parity system. Examples of parity systems may be obtained by combining either, two delta-matroids, or two orthogonal 2-polymatroids, on the same ground-sets. We show that many of the results of Lovász concerning 'double flowers' and 'projections' carry over to parity systems.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.37236/1492</a> <a target="_blank" rel="external noopener" href="">fatcat:nyyqyrpmsffhrcyz4yagal5axm</a> </span>
<a target="_blank" rel="noopener" href="" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href=""> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / </button> </a>